Edexcel 2020 Pure Maths Paper 2 9MA0/02

Edexcel 2020 Pure Maths Paper 2 Question Paper (pdf)

Edexcel 2020 Pure Maths Paper 2 Mark Scheme (pdf)

1. The table below shows corresponding values of x and y for y =
   The values of y are given to 4 significant figures.
   (a) Use the trapezium rule, with all the values of y in the table, to find an estimate for giving your answer to 3 significant figures.
2. Relative to a fixed origin, points P, Q and R have position vectors p, q and r respectively.
   Given that

• P, Q and R lie on a straight line
• Q lies one third of the way from P to R
  show that q = 1/3(r + 2p)

3. (a) Given that
   2log (4 − x) = log(x + 8)
   show that
   x² − 9x + 8 = 0
   (b) (i) Write down the roots of the equation
   x² − 9x + 8 = 0
   (ii) State which of the roots in (b)(i) is not a solution of
   2log(4 − x) = log(x + 8)
   giving a reason for your answer.

4. In the binomial expansion of
   (a + 2x)⁷
   where a is a constant
   the coefficient of x⁴ is 15 120
   Find the value of a.
5. The curve with equation y = 3 × 2^x
   meets the curve with equation y = 15 − 2^x+1 at the point P.
   Find, using algebra, the exact x coordinate of P.
6. (a) Given that
   find the values of the constants A, B and C
   
7. Figure 1 shows a sketch of the curve C with equation
8. A curve C has equation y = f(x)
   Given that

• fʹ(x) = 6x² + ax − 23 where a is a constant
• the y intercept of C is −12
• (x + 4) is a factor of f(x) find, in simplest form, f(x)
  

9. A quantity of ethanol was heated until it reached boiling point.
   The temperature of the ethanol, θ °C, at time t seconds after heating began, is modelled by the equation
   θ = A − Be^−0.07t
   where A and B are positive constants.
   Given that

• the initial temperature of the ethanol was 18°C
• after 10 seconds the temperature of the ethanol was 44°C
  (a) find a complete equation for the model, giving the values of A and B to 3 significant figures.
  Ethanol has a boiling point of approximately 78°C
  (b) Use this information to evaluate the model.

10. (a) Show that
    cos 3A ≡ 4cos³ A − 3 cosA
    (b) Hence solve, for −90°  x  180°, the equation
    1 − cos3x = sin2 x
11. Figure 2 shows a sketch of the graph with equation
    y = 2 | x + 4| − 5
    The vertex of the graph is at the point P, shown in Figure 2.
    (a) Find the coordinates of P.
    (b) Solve the equation
    3x + 40 = 2 | x + 4| − 5
    A line l has equation y = ax, where a is a constant.
    Given that l intersects y = 2| x + 4| − 5 at least once,
    (c) find the range of possible values of a, writing your answer in set notation.
12. The curve shown in Figure 3 has parametric equations
    x = 6sint y = 5 sin 2t 0  t  π/2
    The region R, shown shaded in Figure 3, is bounded by the curve and the x-axis.
13. The function g is defined by
14. A circle C with radius r

• lies only in the 1st quadrant
• touches the x-axis and touches the y-axis
  The line l has equation 2x + y = 12
  (a) Show that the x coordinates of the points of intersection of l with C satisfy
  5x² + (2r − 48) x + (r² − 24r + 144) = 0
  Given also that l is a tangent to C,
  (b) find the two possible values of r, giving your answers as fully simplified surds.

15. A geometric series has common ratio r and first term a.
    Given r ≠ 1 and a ≠ 0
    (a) prove that

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